In thinking about quantum weirdness, it seems to me, that something fundamental in Einstein's theory of relativity tends to get lost -- that nature is four dimensional with time as the forth dimension. The past and future parts of four dimensional reality objectively exist with equal reality separated only by slices of time subjectively experienced as the "present". This understanding tends to be unpopular, even among scientists, because under some interpretations it seems to deny free will.

If we imagine space and time as a solid four dimensional block with events permanently embedded in it we can see that classical events are connected by strands of causality but deduce from evidence that quantum events across space and time are not. (Causality, without which observation would not be possible, is what produces our subjective sense of the present). Importantly, quantum events remain connected by conservation principles. These principles, of course, apply across time but we never thought of this as being "caused" by anything. They are simply fundamental. With classical conservation laws as the precedent we should have been less surprised than we have been by non-causal quantum correlations, "entanglements", that similarly reach across time and space. That we were surprised, I believe, is because we largely failed to think of conservation principles in the four dimensional context.

Let me just add that the "many worlds" interpretation of quantum mechanics effectively adds a fifth dimension to this picture. It solves the mystery of "wave function collapse", which is otherwise inexplicable, by suggesting that there is no collapse, just continuation along multiple fifth dimensional paths of which we can never observe more than one. This is actually quite similar to the way a subjective "present" is singled out for us as unique.

UPDATE: I recently came across mention of a book, A World Without Time: The Forgotten Legacy of Godel and Einsteinby Palle Yourgrau, that corroborates what I said about the unpopularity of the four dimensional space-time of relativity.

In 1942, the logician Kurt Godel and Albert Einstein became close
friends; they walked to and from their offices every day, exchanging
ideas about science, philosophy, politics, and the lost world of German
science. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist.
Einstein endorsed this result reluctantly but he could find no way to
refute it, since then, neither has anyone else. Yet cosmologists and
philosophers alike have proceeded as if this discovery was never made.

I object, however, to use of the ridiculously misleading phrase "time does not exist" in describing the four dimensional space-time view. Obviously, time very much exists as the fourth dimension. The intent must have been to explain that time as commonly understood as a real present but annihilated past and unborn future does not exist.